Update July 23, 2010: Earthquake Forecasts for Four California Cities
In earlier postings, we have shown examples of some new kinds of forecasts that give promise for better capturing the time dependence of earthquake probabilities and forecasts of future activity. Again, these foreasts should be regarded as experimental at this time. These were posted on July 8 and July19, 2010. In this post we continue this process by posting a comparison of 1 year experimental forecasts for four California cities, together with a table that provides numerical comparisons.
The figure below shows the probability in % that a magnitude M>7 earthquake might occur within 150 miles of the indicated city, within 1 year from now. To better facilitate comparison, these figures are plotted together. The proper way to read the figure was given in the posting of July 8, 2010. As the reader can see, the probability generally increases until a major earthquake occurs (blue dot), at which time the probability decreases suddenly. Bursts of small earthquakes within the 150 mile circle lead to sudden increases of probability, while large earthquakes just outside the circle can lead to decreases in probability.
The figure above provides a good view of the long term change in probability, but what about the short term, say, over the past weeks and months? To convey this information, we provide the table below, which gives the probability in % in the first column with numbers, and the change in today's probability from its value 1 week ago, 1 month ago, 3 months ago, 6 months ago, 9 months ago, and 1 year ago.
For example, for the probability that an M>7 earthquake might occur within 150 miles radius around San Francisco, within 1 year from now, is given in the table as 9.41%. The change from 1 week ago is 0.01, meaning that the 1-year probability computed last week was 9.40%. 1 month ago, the 1-year probability was 9.37% corresponding to a change of 0.04%. 3 months ago, the 1-year probability was 9.23% corresponding to a change of 0.18%, and so on. This indicates the probability is increasing with time, leading up to the eventual next earthquake in the future.
Examination of the table shows that for San Francisco and Sacramento, the 1-year probabilty has steadily increased over the past year, while for Los Angeles and San Diego, the 1-year probability has decreased from 6 months ago. This decrease is due to the April 4, 2010 Mexicali (Easter sunday) M7.2 earthquake. Following the sudden decrease at the time of the earthquake, the 1-year probability has begun to increase again to the current values of 9.22% (Los Angeles) and 6.81% (San Diego).
The reader should note that the current 1-year probabilities of 9.41% (San Francisco), 8.53% (Sacramento), 9.22% (Los Angeles), and 6.81% (San Diego) correspond to the vertical values of the red curves in the four plots above when measured at the extreme right hand end of the plots.
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Submitted by Anonymous on Fri, 07/23/2010 - 16:28. #
What does this mean? This is nonsense. and why are the numbers different from the rest of the site?
Submitted by john on Fri, 07/23/2010 - 17:54. #
Thanks for the comment, its a good question.
As explained in the earlier postings, this is an experimental forecast that better captures the time dependent increase in probability leading up to a large earthquake. The present forecast is a method that captures spatial probabilties well, but assumes relatively small temporal changes (you may have noticed this). It is essentially a Poisson-type forecast but modified to include the effects of aftershocks. The present forecast is also based on rates of occurrance of small earthquakes over long periods of time, similar to other current methods. Since rates of small earthquakes can be highly variable in time, large earthquakes are known to occur during periods of low as well as high rates of small earthquakes.
In more technical terms, this experimental forecast is a Weibull probability, which counts the number of small earthquakes since the last large earthquake as a means of determining how far the system has evolved towards the next large earthquake. It therefore measures the accumulation of small earthquakes as an indicator of when the next large earthquake might be, an idea that has not been used previously. It should also be noticed that this forecast has been applied to a circle of fixed radius around four cities (150 miles), a fixed magnitude M>7, and a fixed time period (1 year).
As you can see, this new forecast probability also has the feature that it starts out at a low value following the last large earthquake, generally increases through time, then decreases suddenly after the next large earthquake (although not to zero!). So this new model predicts that while a few large earthquakes will occur soon after the last one, most will occur at much longer times (typically years) after the last one. Generally speaking, the elastic rebound theory of earthquakes, first formulated in 1910 by Harry Fielding Reid, predicts just this type of behavior. The decrease in probability is due to the fact that a large earthquake relieves stress in the immediate region, thereby decreasing the tendency for other large earthquakes to occur in the same area within a short span of time.
In summary, we are constantly looking at new ways to improve our forecasting capability here at Open Hazards. Rather than keeping those new ideas under wraps, we thought it might be interesting to let you see how our thinking is evolving, and to solicit your comments.